How can I select every Nth edge in only one direction on a plane?
You can do this in 3 easy steps:


Edge select one Edge with Alt + RMB.
Click on Select > Checker Deselect (F6 for Nth Selection, Skip and Offset)
Click on Select > Edge Rings




You just have to deselect the top and the bottom edge. In the .gif it is done with Shift + Alt + RMB.

Further Reading on this answer.



Further Information:

After using Checker Deselect you can adjust the desired Nth Selection at the bottom in the Toolshelf Panel or by pressing F6.


  Nth Selection
     &nbsp;&nbsp; Number of points to select.
  Skip
     &nbsp;&nbsp; Number of points to skip.
  Offset
     &nbsp;&nbsp; Offests at what point to start at.


quoted from the Manual